Wind energy has been widely used in recent decades to achieve green and sustainable development. However, wind speed prediction in wind farm clusters remains one of the less studied areas. Spatial features of cluster data of wind speed are not fully exploited in existing work. In addition, missing data, which dramatically deteriorate the forecasting performance, have not been addressed thoroughly. To tackle these tough issues, a new method, termed input set based on wind farm cluster data–deep extreme learning machine (IWC-DELM), is developed herein. This model builds an input set based on IWC, which takes advantage of the historical data of relevant wind farms to utilize the spatial characteristics of wind speed sequences within such wind farm clusters. Finally, wind speed prediction is obtained after the training of DELM, which results in a better performance in forecasting accuracy and training speed. The structure IWC, complete with the multidimensional average method (MDAM), is also beneficial to make up the missing data, thus enhancing data robustness in comparison to the traditional method of the moving average approach (MAA). Experiments are conducted with some real-world data, and the results of gate recurrent unit (GRU), long- and short-term memory (LSTM) and sliced recurrent neural networks (SRNNs) are also taken for comparison. These comparative tests clearly verify the superiority of IWC-DELM, whose accuracy and efficiency both rank at the top among the four candidates.

Probabilistic voltage assessment under multiple contingencies involves numerous network topologies and uncertain operating conditions, resulting in substantial surrogate modeling and computational costs. To address this problem, this paper proposes a voltage-increment-based low-rank (LR) representation with polynomial chaos expansion (PCE), denoted as LR-PCE-ΔV, for a unified multi-contingency voltage assessment. For each model-construction realization, the voltage increment ΔV is calculated as the difference between the post-contingency and pre-contingency bus voltages. The voltage increments under all contingencies are then stacked to form a joint multi-contingency voltage-increment response matrix. Singular value decomposition (SVD) is applied to extract the dominant modes, and one PCE surrogate is constructed for the coefficient of each retained mode. For a new input realization, the predicted modal coefficients are used to reconstruct the voltage increments under all contingencies, after which the corresponding pre-contingency voltages are added to recover the post-contingency voltages. The method is verified on the IEEE 118-bus system with 231 N − 1 contingencies against conventional Monte Carlo simulation (MCS), comprising the pre-contingency AC optimal power flow (ACOPF) and post-contingency AC power flow calculations (ACPF). The proposed method reduces the number of required PCE surrogates from 231 to 21. Compared with the corresponding low-rank model constructed directly from the post-contingency voltages, it reduces the RMSE by 85.9% and achieves a 7.7-fold speedup over conventional MCS while accurately reproducing voltage distributions.